Twist-Bent Bonds Revisited: Adiabatic Ionization Potentials Demystify Enhanced Reactivity

Explicit calculations of vertical and adiabatic ionization potentials of cyclopropane derivatives with modern DFT methods have underscored the possibility of unusually large reorganization energies (defined as the difference between vertical and adiabatic ionization potentials) of 0.5–1.0 eV for several compounds. Such is the case for ionization of the twist-bent σ-bond of trans-bicyclo[4.1.0]hept-3-ene (trans-3-norcarene), for which B3LYP*-D3 calculations predict an adiabatic IP of 7.92 eV. The corresponding value for the cis-norcarene is 8.34 eV. The significantly lower adiabatic IP provides an attractive explanation for the higher reactivity of the trans compound under oxidative conditions. Large reorganization energies are also found for the ionization of cyclopropane, bicyclo[1.1.0]butane, and bicyclo[2.1.0]pentane. In sharp contrast, an exceptionally small reorganization energy is associated with the ionization of tricyclo[1.1.1.0]pentane ([1.1.1]propellane).


■ INTRODUCTION
The middle decades of the 20th century (1925−1975) were arguably the golden age of physical organic chemistry, 1−3 and the concept of strain, 4−6 that is, deviations of bond distances and angles from their normative values, played a key role in the development of the subject. This period also saw the emergence of gas-phase photoelectron spectroscopy (PES) applied to a plethora of organic molecules, which confirmed key predictions from molecular orbital calculations. 7,8 Gas-phase PES proved particularly insightful for strained hydrocarbons and especially for cyclopropane derivatives. 9,10 The theoretical tools available at the time, however, could only provide plausible, rather than conclusive, assignments of the spectra. Herein, accordingly, we have revisited the lowest ionization potentials (IPs) of selected cyclopropane derivatives with modern DFT calculations with a view to reliably characterizing the lowest ionized states (Scheme 1). 11−17 The photoelectron spectra of cyclopropane derivatives are chock-full of subtleties and mysteries. 9,10 Thus, while cyclopropane exhibits an experimental IP of 9.86 eV, 18 23 as is that of the potentially less strained cisbicyclo[4.1.0]hept-3-ene (cis-3-norcarene), 9.05 eV. 24 As it happens, trans-bicyclo [4.1.0]hept-3-ene (trans-3-norcarene) exhibits an essentially identical vertical IP, 9.00 eV. 24 In other words, our intuitive ideas about angle strain are a poor guide to the PES data, which brings us to the subject of bent bonds and, in particular, twist-bent bonds. 25−27 Cyclopropane provides arguably the best-known example of bent bonds, in which the interorbital angle for C−C bonds (104−105°) is much wider than the internuclear bond angle (60°). 28,29 Accordingly, the path of maximum electron density between two carbons curves outside the CCC equilateral triangle approximately in the form of a banana, which has led to the moniker "banana bonds" for the CC bonds in cyclopropane. Over 50 years ago, 30,31 Gassman recognized that the ring-fusion bond in strained trans-fused cyclopropane derivatives such as norcarane exhibits an altogether different topology. Seen from the cyclopropane carbon atom across the ring-fusion bond, the latter is found to exhibit a sigmoidal topology, 30,31 as depicted in Scheme 2.
Gassman described the two topologies as "symmetrically bent" and "twist-bent", 30,31 even though the latter also exhibits approximate C 2 local symmetry in terms of Mislow's terminology on local symmetry groups. 32 Some may choose to analogize a twist-bent bond to an incipient conrotatory ringopening of a cyclopropane. 33 Working primarily with trans-3norcarene derivatives, Gassman and co-workers showed that the twist-bent bond is significantly more reactive than the normal ring-fusion bond in cis-3-norcarene. 34−36 How then can we understand that cis-and trans-3-norcarene exhibit essentially identical vertical IPs? 24 Early DFT calculations, published posthumously for Gassman, showed that although the lowest vertical IP corresponds to the twist-bent ring-fusion bond for the trans isomer, it corresponds to the C−C π-bond (i.e., a part of the C−C double bond) at the 3-position in the cis isomer. 24 The present B3LYP* calculations confirm this conclusion but also shed additional light on the subject.

■ RESULTS AND DISCUSSION
In this study, we have examined six cyclopropane derivatives and their ionized states with B3LYP* 37,38 -D3 39 /ZORA 40 -STO-QZ4P calculations and the ADF 2019 program. 41 Table 1 lists calculated vertical and adiabatic IPs and also the corresponding experimental values, when available. Figure 1 depicts the optimized geometries of the neutral and cationic states, the spin density profiles of the optimized cations, and 2−3 HOMOs of the neutral molecules. The calculated IPs generally agree with experimental values to within 0.2−0.3 eV, while differences in IPs among different molecules are in even better agreement with experiment. Overall, the calculations do a good job of reproducing the somewhat perplexing trends in IPs mentioned above.
A key new insight from this work is that large reorganization effects may be involved for ionization of many, but not all, cyclopropane derivatives. In other words, the neutral and cationic states may differ significantly, even dramatically, in terms of their geometries. Understandably, the adiabatic IPs in such cases may be dramatically lower than the vertical IPs. Thus, upon ionization, one of the ionized bonds of cyclopropane expands from 1.506 to 1.891 Å (Figure 1), that is, by almost 0.4 Å, consistent with a 0.75 eV difference between experimental vertical and adiabatic IPs, which have been reported as 9.86 18 30 eV), which corresponds to a reorganization energy of almost 1 eV! It is worth noting that the relevant experimental value (8.6 eV) quoted in Table 1 is not for the same compound but for the structurally related bicyclo[2.1.0]pent-2-ene. 42 As in the case of cyclopropane, the large reorganization energies appear to be clearly related to large geometrical changes accompanying ionization. In sharp contrast, only a very small reorganization energy is associated with the ionization of tricyclo[1.1.1.0]pentane ([1.1.1]propellane); the optimized DFT geometry, consistent with our rationale, reveals only a small shrinkage of the central C−C bond upon ionization (Figure 1), a consequence of the remarkable polycyclic structure. 22 In the case of the 3-norcarenes, the adiabatically ionized states of both the cis and trans isomers are similar in that both involve ionization of the ring-fusion bond, unlike in the vertically ionized states, where the ionization occurs from different orbitals, as mentioned above. This difference may be seen from the singly occupied MOs (SOMOs) of the two cations ( Figure 2) and from the spin density plots included as part of Figure 1

ACS Omega
http://pubs.acs.org/journal/acsodf Article derivatives examined in this study, a good 0.4 eV lower than that of cis-3-norcarene, which appears to dovetail with a significant difference in the spin density profiles of the two cations. Thus, most of the spin density in the trans-3-norcarene cation has drained out of the internuclear region of the ionized bond (in much the same way as in the majority of the other compounds studied), whereas the spin density in the cis-3-norcarene cation is still substantially concentrated in the internuclear region. We suggest that the difference in adiabatic IP and topological